W*-superrigidity of mixing Gaussian actions of rigid groups

Rémi Boutonnet (1)

1 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées

We generalize W *-superrigidity results about Bernoulli actions of rigid groups to general mixing Gaussian actions. We thus obtain the following: If Γ is any ICC group which is w-rigid (i.e. it contains an infinite normal subgroup with the relative property (T)) then any mixing Gaussian action Γ X is W *-superrigid. More precisely, if Λ Y is another free ergodic action such that the crossed-product von Neumann algebras are isomorphic L ∞ (X) ⋊ Γ ≃ L ∞ (Y) ⋊ Λ, then the actions are conjugate. We prove a similar statement whenever Γ is a non-amenable ICC product of two infinite groups.

Mots clés: deformation/rigidity; W*-superrigidity

Domaines: Algèbres d'opérateurs [math.OA]

Rémi Boutonnet. W*-superrigidity of mixing Gaussian actions of rigid groups. Advances in Mathematics, 2013, 244, pp.69 - 90. ⟨10.1016/j.aim.2013.05.012⟩. ⟨hal-01447552⟩